Fuzzy Fixed-Time Learning Control With Saturated Input, Nonlinear Switching Surface, and Switching Gain to Achieve Null Tracking Error

A class of generalized nonlinear dynamic systems is first approximated by N fuzzy-based linear subsystems using the identification of input-output data or the linearizing system with respect to suitable operating points. To obtain null trajectory tracking error in fixed time, a fuzzy fixed-time control (FFTC) with nonlinear switching surface and switching gain is first designed. It can be said that the FFTC is based on a class of passive and distributive models with uncertainties. To compensate enormous uncertainties, a fuzzy fixed-time learning control (FFTLC) by learning two unknown coefficients for the upper bound of uncertainties in each subsystem is designed. As compared with radial basis function neural network, the computational complexity for the compensated uncertainties is much simple. It can be said that an FFTLC is based on a class of online active and distributive uncertain models. Due to the fixed-time control design, the transients often occur, particularly for the larger uncertainties or initial tracking error. Hence, the saturated input of nonlinear dynamic system is addressed and online compensated. Finally, the compared simulations and application to two-link robot manipulator confirm the effectiveness, robustness, and less computation as compared with previous studies.